iDevices are designed to be linked to an iTunes library where they get their content. If you've never trusted iTunes before and been manually copying items onto your iDevice then you're just making it hard on yourself.
Synchronizing your files and upgrading the iOS are separate steps. I would recommend you get the iPad linked to your iTunes library properly and synchronization figured out before trying to upgrade lest you lose your iPad content in the process.
First, make sure your iTunes and your iPad are registered to the same AppleID you used to download your apps and other iTunes store items. (This may already be the case if it's telling you about purchases, but check.)
Next, download your past purchases to your Mac.
For other items like your own music and video files, the synchronization is one-way. If they're not in your iTunes then they won't sync back from your iPad.
Try using manual mode for those items if you're happy leaving well enough alone with keeping those items on your iPad.
Otherwise, you'll have get these from your original source (ideally) or use a third-party utility to extract the files from the device. It's been a while since I've had to do that myself, but as I recall it was a bit messy since the files lost their original filenames when they were stored in the device's filesystem/database. At least I think you can get them out somehow, but yes, it might be buggy.
The key is to have everything in iTunes before allowing the iOS upgrade to remove anything from the iPad. In my own experience, everything was right back where it was after the iOS upgrade, even though I had some similar warnings, but if you don't already have the items in iTunes then it might be a different story.
Best Answer
Sorry to hear about your stroke. To answer your question, downgrading operating system installs are pretty tricky. This is further complicated by Apple's switch to exclusively distribute OS X via the App Store - if you don't already have access to the Mavericks installer, you're out of luck given that you can't even get the installer on the App Store anymore.
If you do have access to the Mavericks installer, you'll need to back up your documents somewhere as you will need to completely erase the hard drive in your Mini before installing Mavericks. If you use Time Machine to backup, this could be an option - but I couldn't be certain as I've never downgraded from Yosemite to Mavericks and I know that Time Machine backs up the OS as well, so there could be some issues involved.
Once that's done, you can then bring over your documents and reconfigure your apps (if you have iCloud and sync your Apple app settings, that should be effortless - but I can't confirm as, again, I've never done the downgrade).
If this sounds like a royal pain in the butt … you're right. Yosemite is a pretty big change from OS X, but if you can stand to stick with it that will probably be your best option.